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Null and Alternative Hypotheses01:16

Null and Alternative Hypotheses

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The actual hypothesis testing begins by considering two hypotheses. They are termed  the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.
The null hypothesis, denoted by H0 is a statement of no difference between the variables—they are not related. This can often be considered the status quo. As  a result if you cannot accept the null, it requires some action.
The alternative hypothesis, denoted by H1 or Ha, is a claim about the...
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Alternative RNA Splicing02:18

Alternative RNA Splicing

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Alternative RNA splicing is the regulated splicing of exons and introns to produce different mature mRNAs from a single pre-mRNA. Unlike in constitutive splicing where a single gene produces a single type of mRNA, alternative splicing allows an organism to produce multiple proteins from a single gene and plays an important role in protein diversity.
There are five types of alternative RNA splicing that vary in the ways the pre-mRNA segments are removed or retained in the mature mRNA. The first...
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Poisson's Ratio01:23

Poisson's Ratio

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Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign...
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Odds Ratio01:09

Odds Ratio

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The odds ratio (OR) is a statistical measure used extensively in epidemiology and research to quantify the strength of association between exposure and outcome across different groups. Unlike relative risk, which compares the probabilities of an event occurring, the odds ratio compares the odds of an event occurring in the exposed group to the odds of it occurring in the unexposed group. The odds, in this context, are calculated as the probability of the event happening divided by the...
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Hazard Ratio01:12

Hazard Ratio

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The hazard ratio (HR) is a widely used measure in clinical trials to compare the risk of events, such as death or disease recurrence, between two groups over time. It reflects the ratio of hazard rates—the instantaneous risk of the event occurring—between a treatment group and a control group. This measure provides valuable insights into the relative effectiveness of a treatment by assessing how the risk of an event differs between the two groups.
For example, in a clinical trial...
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The Ratio of X Chromosome to Autosomes02:45

The Ratio of X Chromosome to Autosomes

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In most organisms, sex is determined by the ratio of X and Y chromosomes. However, in some organisms, such as Drosophila and C.elegans, sex is determined by the ratio of the number of X chromosomes to the number of sets of autosomes. The Y chromosome in Drosophila is active but does not determine sex. It contains genes responsible for the production of sperms in adult flies.  
Normal male Drosophila has a ratio of one X chromosome to two sets of autosomes. In contrast, normal female...
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Related Experiment Video

Updated: Feb 6, 2026

Identification of Alternative Splicing and Polyadenylation in RNA-seq Data
08:35

Identification of Alternative Splicing and Polyadenylation in RNA-seq Data

Published on: June 24, 2021

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On the alternative hypotheses for the win ratio.

Lu Mao1

  • 1Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin-Madison, K6/428 Clinical Sciences Center, 600 Highland Avenue, Madison, Wisconsin 53792, U.S.A.

Biometrics
|August 11, 2018
PubMed
Summary

This study expands the win ratio method to include upper quadrant stochastic order, broadening its applicability. This enhances consistency for a wider range of alternative hypotheses, including those from copula models.

Keywords:
Composite endpointConsistencyCopula modelSemi-competing risksStochastic order

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Area of Science:

  • Statistics
  • Biometrics
  • Survival Analysis

Background:

  • The win ratio is a statistical measure used for comparing treatment effects.
  • Previous work by Luo et al. (2015) established win ratio consistency for hazard order alternatives.
  • A limitation was the exclusion of certain alternative hypotheses, particularly those from copula models.

Purpose of the Study:

  • To extend the theoretical framework of the win ratio.
  • To investigate the win ratio's consistency under the upper quadrant stochastic order.
  • To incorporate a broader class of alternative hypotheses, including copula-based alternatives.

Main Methods:

  • Mathematical extension of existing win ratio theory.
  • Application of stochastic order theory to bivariate distributions.
  • Analysis of win ratio consistency under upper quadrant dominance.

Main Results:

  • The win ratio is shown to be consistent against the upper quadrant stochastic order.
  • This extends the range of detectable treatment effects beyond simple hazard orders.
  • The framework accommodates alternatives arising from common copula models previously excluded.

Conclusions:

  • The win ratio offers robust consistency under a wider set of alternative hypotheses.
  • The findings broaden the utility of the win ratio in clinical trials and other comparative studies.
  • Potential for generalization to multivariate and stratified win ratio analyses was discussed.